Mathematical Digest

Short Summaries of Articles about Mathematicsin the Popular Press

The discovery of quasicrystals presented scientists with a puzzling class of materials. The atoms of these metal alloys areneither arranged in neat rows, as in crystals, nor scattered randomly,as in glass. Recently, Paul Steinhardt and Hyeong-ChoiJeong proposed a novel mathematical model that promised to shed light on the construction of quasicrystals.

Extending the work of other researchers, who first considered thetilings of Roger Penrose, Steinhardt and Jeong postulated thatneighboring clusters in a quasicrystals share atoms. Moreover, themodel they created predicts that quasicrystals have a simplicity morelike that of crystals than was previously recognized.

This model has been compared to electron microscope data and found to have aremarkably precise correspondence.